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Properties

Label 8.12.b
Level $8$
Weight $12$
Character orbit 8.b
Rep. character $\chi_{8}(5,\cdot)$
Character field $\Q$
Dimension $10$
Newform subspaces $1$
Sturm bound $12$
Trace bound $0$

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Defining parameters

Level: \( N \) \(=\) \( 8 = 2^{3} \)
Weight: \( k \) \(=\) \( 12 \)
Character orbit: \([\chi]\) \(=\) 8.b (of order \(2\) and degree \(1\))
Character conductor: \(\operatorname{cond}(\chi)\) \(=\) \( 8 \)
Character field: \(\Q\)
Newform subspaces: \( 1 \)
Sturm bound: \(12\)
Trace bound: \(0\)

Dimensions

The following table gives the dimensions of various subspaces of \(M_{12}(8, [\chi])\).

Total New Old
Modular forms 12 12 0
Cusp forms 10 10 0
Eisenstein series 2 2 0

Trace form

\( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + O(q^{10}) \) \( 10 q + 22 q^{2} + 436 q^{4} - 24308 q^{6} - 33616 q^{7} - 208472 q^{8} - 472394 q^{9} + 29864 q^{10} - 476216 q^{12} + 2264272 q^{14} + 3391792 q^{15} + 3757072 q^{16} + 2639732 q^{17} + 2329130 q^{18} + 8296432 q^{20} - 24201892 q^{22} - 45357808 q^{23} + 10668944 q^{24} - 41502654 q^{25} - 101931080 q^{26} - 95722144 q^{28} + 261362768 q^{30} + 442035392 q^{31} + 343908512 q^{32} - 54732216 q^{33} - 187103796 q^{34} - 431195700 q^{36} + 375100844 q^{38} - 431459312 q^{39} + 1519138784 q^{40} - 654907964 q^{41} - 3697737056 q^{42} - 4127012952 q^{44} + 6028867440 q^{46} - 560226528 q^{47} + 9357606048 q^{48} + 1143661722 q^{49} - 9626584226 q^{50} - 11595427248 q^{52} + 20050494008 q^{54} + 5632783984 q^{55} + 18698733760 q^{56} - 783862360 q^{57} - 22828679464 q^{58} - 43681325472 q^{60} + 40774631744 q^{62} - 14483624624 q^{63} + 55266728512 q^{64} - 80291360 q^{65} - 83128448712 q^{66} - 83303223768 q^{68} + 100120831168 q^{70} - 11769460176 q^{71} + 112862051672 q^{72} + 32304890372 q^{73} - 102103996184 q^{74} - 97501928568 q^{76} + 144445560944 q^{78} + 57291670496 q^{79} + 128322038976 q^{80} - 23172996094 q^{81} - 123309929604 q^{82} - 199990865984 q^{84} + 130201908124 q^{86} - 73844404272 q^{87} + 169216119632 q^{88} - 108276011804 q^{89} - 228506434984 q^{90} - 141139403232 q^{92} + 145336130016 q^{94} + 70146835376 q^{95} + 109508068928 q^{96} + 60995282900 q^{97} - 6194726778 q^{98} + O(q^{100}) \)

Display 100 coefficients 10 coefficients

Decomposition of \(S_{12}^{\mathrm{new}}(8, [\chi])\) into newform subspaces

Label Char Prim Dim $A$ Field CM Traces Sato-Tate $q$-expansion
$a_{2}$ $a_{3}$ $a_{5}$ $a_{7}$
8.12.b.a 8.b 8.b $10$ $6.147$ \(\mathbb{Q}[x]/(x^{10} - \cdots)\) None \(22\) \(0\) \(0\) \(-33616\) $\mathrm{SU}(2)[C_{2}]$ \(q+(2+\beta _{1})q^{2}+(\beta _{1}+\beta _{3})q^{3}+(43+2\beta _{1}+\cdots)q^{4}+\cdots\)